(a)
To show that the expected value represented by the counter after n INCREMENT operations that have been performed is exactly n.
(a)
Explanation of Solution
Given Information: The INCREMENT operation works on a counter containing the value i in a probabilistic manner. If
Explanation:
The counter after n INCREMENT operations is performed exactly n times for the expected value.
Consider that the initial value of the counter is i and increasing the number representation from
The expected increase is calculated as,
Hence, the expected increment represented by the counter is 1.
(b)
To calculate the variance in the value represented by the register after n INCREMENT operations have been performed.
(b)
Explanation of Solution
Given Information: Consider a simple case:
Explanation:
Consider that
Since
The value represented increases by 100. Therefore, by the equation (C.27)
Now, adding the variances of the
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Chapter 5 Solutions
Introduction to Algorithms
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